Deriving a Vector Expression from Given Direction

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SUMMARY

The discussion centers on deriving a vector expression from the directional information provided by the equations dx=2, dy=-2, and dz. The user seeks assistance in formulating a vector representation for the directional derivative of a scalar function based on these parameters. The key takeaway is that the user needs to convert the directional ratios into a vector format, which can be achieved by normalizing the direction vector derived from the given ratios.

PREREQUISITES
  • Understanding of vector representation in three-dimensional space
  • Knowledge of directional derivatives in multivariable calculus
  • Familiarity with partial derivatives and their applications
  • Basic proficiency in vector normalization techniques
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  • Study how to derive directional derivatives using vector calculus
  • Learn about vector normalization and its importance in directional analysis
  • Explore examples of converting directional ratios into vector forms
  • Investigate the application of partial derivatives in multivariable functions
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Students and professionals in mathematics, particularly those studying multivariable calculus, as well as anyone involved in vector analysis and optimization problems.

Drain Brain
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How can you derive an expression from the given direction defined by dx=2dy=-2dz. This is just a part of a problem that I'am solving. I have no idea how to get a vector expression using the given info. please help. Thanks!

by the way I'm trying to find the directional derivative of a certain scalar function in the direction given above. By I don't know how to get a vector representayion of the given direction. Please help me!
 
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is that possible? use derivative.
 
What? I Know that I would use partial derivative here. But what I need help with is finding the vector representation of the given direction. Please anybody knows how to do it tell me. Thanks.!
 
Hey guys, do you have any idea on how to do this? I want to know it so badly. Please give me an insight.
 

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